A note on the local regularity of distributional solutions and subsolutions of semilinear elliptic systems
A note on the local regularity of distributional solutions and subsolutions of semilinear elliptic systems
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DOI：
10.1007/s00229-017-0917-8
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发表时间：
2017-02
影响因子：
0.6
通讯作者：
Rainer Mandel
中科院分区：
文献类型：
--
作者：
Rainer Mandel
本文证明了半线性椭圆型方程组L_k^mu_k = f_k（x，u_1，\ldots，u_N）\quad\text{in }\mathbb{R}^n\qquad（k= 1，\ldots，N）$$的分布解和子解的局部正则性结果，其中f_k（x，u_1，\ldots，u_N）和f_k（x，u_1，\ldots，u_N）是发散形式的.我们证明了分布子解是局部有界的，如果。进一步给出了子解的正则性和有界子解的改进形式。即使对于我们的结果是新的。
In this note we prove local regularity results for distributional solutions and subsolutions of semilinear elliptic systems such as $$ L_k^m u_k = f_k(x,u_1,\ldots,u_N) \quad\text{in }\mathbb{R}^n\qquad (k=1,\ldots,N) $$ whereare of divergence-form and. We show that distributional subsolutions are locally bounded from above iffor. Furthermore, regularity properties of subsolutions and improved versions for bounded subsolutions are given. Even forour results are new.